Randomized benchmarking with gate-dependent noise

Abstract

We analyze randomized benchmarking for arbitrary gate-dependent noise and prove that the exact impact of gate-dependent noise can be described by a single perturbation term that decays exponentially with the sequence length. That is, the exact behavior of randomized benchmarking under general gate-dependent noise converges exponentially to a true exponential decay of exactly the same form as that predicted by previous analysis for gate-independent noise. Moreover, we show that the operational meaning of the decay parameter for gate-dependent noise is essentially unchanged, that is, we show that it quantifies the average fidelity of the noise between ideal gates. We numerically demonstrate that our analysis is valid for strongly gate-dependent noise models. We also show why alternative analyses do not provide a rigorous justification for the empirical success of randomized benchmarking with gate-dependent noise.

It measures what you expect. Comments welcome. v2: removed an inconsistent assumption from theorem 3 and clarified discussion of prior work. Results unchanged. v3: further clarified discussion of prior work, numerics now available at https://github.com/jjwallman/numerics. v4: licence change as required by Quantum

References in corpus (8)

• Randomized Benchmarking of Quantum Gates
• Robust randomized benchmarking of quantum processes
• Direct Fidelity Estimation from Few Pauli Measurements
• Quantum Tomography via Compressed Sensing: Error Bounds, Sample Complexity, and Efficient Estimators
• Symmetrised Characterisation of Noisy Quantum Processes
• Process verification of two-qubit quantum gates by randomized benchmarking
• What randomized benchmarking actually measures
• Accelerated Randomized Benchmarking

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